Abstract
In this talk we apply a novel approach to the exploration of energy landscapes. In many covalent atomic systems, the potential energy V = V0 + V1 can be separated into a dominant term V0 and a smaller term V1. The dominant term V0 involves covalent bond lengths and angles. These are initially set equal to infinity, which allows them to be treated as constraints. Such constraints fix the bond lengths and bond angles and allow us to use theorems from graph theory to perform a rigid region decomposition of the network of atoms, which identifies the rigid regions, the flexible joints between them and also the stressed regions. This approaches facilitates finding the actual energy landscape associated with the full potential, as shown in the following examples: In flexible molecules, the energy landscape can have multiple regions, each containing multiple minima. We show movies of the motion in small and large flexible macromolecules. In glasses, we can identify polymeric glasses and amorphous solids by tracking the mean coordination. In some cases an intermediate phase can occur which is rigid but unstressed. By including double bonds, hydrophobic tethers and hydrogen bonds appropriately into V0, we can extend this approach to proteins, where local flexibility is often related to biological function. The protein folding transition is another example of a floppy to rigid transition and is more first order than second order because of the self-organized nature of the cross-linked polypeptide chain in the native protein.
Support is acknowledged from NSF, DOE and NIH.

References

M. F. Thorpe, D. J. Jacobs, M. V. Chubynsky and J. C. Phillips Self ­ Organization in Network Glasses J. Non­Cryst. Sols. 266­269, 859­866 (2000).

M. F. Thorpe, Ming Lei, A. J. Rader, Donald J. Jacobs and Leslie A. Kuhn Protein Flexibility Predictions using Graph Theory Proteins 44, 150 - 165, (2001).

More details of this work can be found via http://www.pa.msu.edu/~thorpe/